This screen is like the capture in Pokémon GO where you have the Pokémon and just throw the ball at it. This is done with the Joy-Cons motion detection in Docked Mode or using motion or the control stick in Handheld mode. The better the throw into the circle around the Pokémon, the better the chance of capture
There are, however, ways of improving the odds of capture. First up is the way you throw. With all the Pokémon, there's a giant circle which shrinks down and if you hit in the middle of the circle, you'll get a special bonus which improves the rate of capture. There are three levels to this.
In addition to that, if you're playing in local co-op play and both players throw the ball and it hits at the same time, you'll get a boost due to the Synchronized capture.
Finally, there are three different berries that improve the rate of capture. Each Berry has a higher boost making capture a lot easier than standard.
Finally, there's another method that helps the catch rate. As you increase your catches of the same species of Pokémon, the capture rate will increase. This does not have to be within a combo.